LT 21 Proceedings of the 21st International Conference on Low Temperature Physics Prague, August 8-14, 1996

Part S1 - Quantum Fluids and Solids: Liquid Helium

H e a t T r a n s p o r t E x p e r i m e n t s in S u p e r f l u i d H e l i u m

Daniel Murphy and Horst Meyer

Department of Physics, l)ukc University Durham, North Carolina, 27708-0305 USA

New measurements of the boundary resistance in superfluid 4Ile (2 ppb 3Ile) near Tx are reported in a cell of improved design with parallel polished copper surfaces. In contrast to several previous experiments, the large Q-dependent boundary resistance anomaly observed previously was no longer detected. However the small, weakly divergent boundary resistance was observed and the results are compared with previous experiments and predictions. Measurements with this new ecll of the thermal conductivity and relaxation times in dilute superfluid mixtures of 3He in 4He are reported above 1.5 K. They confirm predictions for the bulk fluid; the diffusion coefficients Diso for isolated 3Hc impurities so obtained are then internally consistent.

1. I N T R O D U C T I O N

The boundary resistivity of superfluid 4lie near T~ shows a weakly diverging singafiarity, which w~Ls first observed by Duncan, Ahlcrs and Steinberg [1][2]; these early results arc in agreement with current predictions[3]. However the measurements by Dun- can et al., as well as others in this laboratory[d],[5], showed in addition a much larger Q-dependent anomaly of Rb, supcrposcd on the weaker one, which was not understood. We now believe that this lat- ter anomaly is an instrumental effect resulting from heat flow in the cell's sidewall gap. Furthermore we suspect that this gap also caused the unexplained re- suits in the measurement of transport properties of very dilute superfluid 3Ite-4He mixtures[6}.

In this paper we report measurements of the boundary resistivity Rb in 4l-le (X(3He) = 2 ppb), using a conductivity cell with parallel copper faces. Wc have used a design where great care was taken to suppress any gap between the copper pieces and the stainless steel spacer. A detailed description of the new cell and a discussion of previous results on Rb are presented in ref.[8], hirthermore we report mea- surements in dilute 3He-4 He mixtures of the thermal conductivity and the corresponding rclaxatkm times in the approach to steady state or equilibrium.

2. R E S U L T S

2 . 1 . 4 H e b o u n d a r y res is tance near T~

The weak anomaly of/~b orlly manifi;sts itself for reduced temperatures of the fluid layer [~[ < 4 x

10 -3, where ~ = (~' - T~,)/T,x. Here we have defined 7 ~ = Ttop + AT/2, where Ttop is the temperature of the top part of the cell and AT is the temperature difference between the top and bottom parts. In the measurement procedure, Ttop was increased by small steps under a steady heat flux Q (between 1 and 80 p.W/cm 2) from [e[ = 5 x 10 -3, and AT was recorded until at a sharply defined value Tt*op it suddenly rose to a large value of the order of millidegrees, which marked tile breakdown of the superfluid phase. The results of these experirnents are shown in Fig.1 where Rb is plotted as a function of [el for three vahms of Q. The dashed line is the background resistivity which ~.xtrapolates to Rb,o at Tx. The solid line represents tile prcdictions by Frank and Dohm [3]. We note that in contrast to previously published experiments [1],[2],[4],[5], but in agreement with those by Li[7],the large Q-dependent anomaly is not observed.

The measurcd divergence is larger than predicted [3], and also is larger than that measured by Duncan and Ahlcrs [2] in cells where the large Q-dependent anomaly was observed. However a proposed inter- pretation of their reported Rb data as well as those of ref[5] in terms of heat flow through the sidewall faces as well as through the parallel flat faces, indi- cates that the effective boundary area during these experiments is larger than was assumed. If this in- terpretation is correct, the reported Rb data should be rcscaled by a vahm representing the ratio of the effcctiw: area to the assumed boundary area. When this is done, the agreement between the results for the c(,.lls K ,L2 of [2] and the present one is good [8].

Czechoslovak Journal of Physics, Vol. 46 (1996), Suppl. $1 '7'7

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Figalre 1: The boundary resistivity Rb versus the re- duced temperature kl for three wdues of the heat flux Q, as indicated by symbols. Solid line: predictions by Frank and Dohrn[3]. l)otted line: background Rb,o(T) extrapolated to Tx

2.2. The rma l c o n d u c t i v i t y and relaxat ion t ime in superf lu id 3He-4He mixtures

For mixtures with molefractions X < I x l0 -2, at temperatures where the contribution to the conduc- tivity from counterflow is much larger than that frorn difhlsion, the effective conductivity neff is shown by the theory of F.London and of I.M. l(halatnikov to be njr c~ Diso X X -1. Here Diso is the mass dif- fusion coefficient of isolated 3lie impuritics in alle, which is determined by the impurity scattering by the excitations in aHe, and therefore independent of X. Furthermore the time constant r0 of the slowest mode in the thermal relaxation process via diffusion is shown to be r0 or h 2 x (Oiso) -1. (The complete equations and references for both neff and r0 are pre- sented in ref.[6]). Hence the steady-state conductiv- ity and the relaxation experiments permit a dmck of the internal consistency of the derived vahm of Diso. We have performed rneasurcrnents over the temper- ature range 1.4 < T < 2.17K and for mixtur(~s with molefraction X between l0 -6 and l0 -3. Wc lind indeed that for X > 5 x l0 -4 the experiments arc in agreement with the predictions and that the wd- ues of Diso from the two measurements are internally consistent. In Fig.2 we present the values of Di~, ob- tained both from conductivity and from relaxation experiments for X = 6 x 10 -4 as a flmction of T. There is good agreement between these two data sets. A detailed analysis of the results will be prtmented

31 -o~176 o,rom o

~ - - 10.49[,_ 1~ A -

1.7 1.g 1.9 2.0 2.1

T (K)

Figure 2: Mass diffusion coefficient Diso as obtained from ~efr (open squares) and from r0 (open circles) for a superfluid dilute mixture with X(3He) -- 6.0 • 10 -4 as a fimction of T

elsewhere[8]. In previous measurements with cells having a narrow sidewall gap[4][6], the derived Dido from neff and ro were not consistent. We can again explain these anomalous observations by heat flow through the sidewall gap. A detailed explanation is to bc presented in [8].

Wc greatly appreciate discussions with G. Ahlers, R.P. Bchringcr, R.V. Duncan, J.A. I,ipa, J.D. Reppy, K. Sdlwarz, J.A.Tough, and F. Zhong.

Refe rences

[1] 1LV. Duncan, O. Ahlers and V. Steinberg, Phys. Rev. Lett. 58, 377 (1987).

[2] R.V. Duncan and O. Ahlers, Phys. Rev. B 43 , 7707 (1991).

[3] D. Frank and V. Dohm, Z. Phys. B 84, 443 (1991) and refercnces therein.

[4] F. Zhong, J. Tuttle and H. Meyer, J. Low Temp. Phys. 79, 9 (1990).

[5] D. Murphy and H. Meyer, J. Low Temp. Phys. 65, 185 (1994).

[6] D. Murphy and H. Meyer, J. Low Temp. Phys. 9 9 , 7 4 5 (1995).

[7] Q. Li, Phi). Thesis, Stanford University (1990) (unpublished). J.Lipa (private communication)

[8] D. Murphy and H. Meyer, (to be published).

78 Czech. J. Phys. 46 (1996), Suppl. $1